1. Field of the Invention
The invention relates to the field of data processing. More specifically, the invention relates to encoding.
2. Background of the Invention
Typically, mathematical and engineering systems use a decimal system and/or binary system to represent numbers and to perform calculations. Over time, alternative numeration systems have been developed for different applications. Such numeration systems include fixed-radix, mixed-radix and mixed-base.
A fixed-radix numeration system has a constant radix for all positions of a sequence of digits. In fixed-radix numeration systems, the weights of successive positions are successive integral powers of a single radix, multiplied by the same factor. Examples of fixed-radix numeration systems include decimal, binary and hexadecimal systems.
A mixed-radix numeration system is a radix numeration system in which all radices of each position of a sequence of digits are constant, but not necessarily the same. The mixed-radix numeration system is a more general numeration system in which there may not be integral ratios between the radices of all digits. For example, time is measured with a mixed-radix numeration system. Hours are measured in tens of minutes and minutes having radices 6 and 10 respectively.
In a mixed-based numeration system, numbers are represented as the sum of a sequence of position values. Each position consists of a mantissa and a base. The base of a given position is constant for a given application, but the bases across positions are not necessarily integral ratios between the radices of all the positions. For example, years are measured with a mixed-base numeration system. Years are measured with tens of months and months having bases 12:10:1.
The above numeration systems are satisfactory methods to represent numbers, but are inefficient for modeling operation sequences. The above numeration systems are also inefficient for transmission of data in some special cases.